Section 5.2 Properties of Rational Functions

Name: ______Period:______

Sections 5.2 and 5.2 Guided Notes Lesson will be on October 15, 2013

Instructions: Study sections 5.2 and 5.3 in your book or from my notes on Canvas or my webpage. Fill in the missing information in the notes. On Tuesday, October 15 we will focus on doing problems in class, which will include examples as well as some homework problems. The idea of this activity is to help use class time for hands on practice with the concepts.

Section 5.2 – Properties of Rational Functions

A rational function is a function of the form

Where _____ and _____ are polynomial functions and ____ is not the zero polynomial. The ______of a ______function is the ______of all ______except those for which the ______is ______.

Example 1 –

(A) Explain how they got the domain of

(B) Explain how they got the domain of .

If ______is a rational function and if _____ and q have no common factors, then the

______function R is said to be in ______. For a rational function

______in lowest terms, the ______, if any, of the ______in the domain of R are the ______of the graph of R and so will play a major role in the graph of R. The real zeros of the ______of R [that is, the numbers x, if any, for which q(x) =

__], although not in the domain of R, also play a major role in the graph of R.

Read through Example 2 – we will go over it again in class. Read through example 3 – we will go over it again in class.

Asymptotes

In Figure 30, you are given four different graphs that demonstrate asymptotes. In your own words, explain what happens to the graph R(x) as it approaches the line y = L and explain what asymptote y=L is.

Which kind of asymptote(s) may a graph intersect? ______

Which kind of asymptote will a graph never intersect?______

What is the third possible asymptote? ______

What kind of line is this third asymptote? ______Find the vertical asymptotes in example 4 for parts b and c. b)

If a rational function is proper, that is, if the ______of the numerator is ______than the degree of the ______, then as ______or as ______the value of R(x) approaches _____. Consequently, the line ______(the ______) is a horizontal ______of the graph.

Example 5 – explain why y = 0 is a horizontal asymptote.

If a rational function ______is improper, that is, if the ______of the

______is greater than or ______to the ______of the ______, we use long division to write the rational function as the sum of a polynomial f(x) (the quotient) plus a

______rational function ______(r(x) is the remainder). That is we write Where f(x) is a ______and ______is a proper rational function. Since ______is proper, ______(which means r(x)/q(x) approaches 0) as ______or as

______. As a result,

The possibilities are listed next. State these possibilities in your own words, go through examples 6 – 8 to help you write them in your own words.

Section 5.3 – The Graph of a Rational Function

Part 1 – Analyze the graph of a Rational Function

List the Step – by – Step Solution and briefly explain how each step affects the graph (Look through examples 1 – 5).

Step 1

Step 2

Step 3 Step 4

Step 5

Step 6

Step 7

Step 8

Constructing the Function from the Graph or problem:

Walk through examples 6 and 7 – Now write your own steps to follow construct a function from a graph or word problem.